Napoli dominated the second half as substitute Dries Mertens also deflected an effort on to the crossbar.
The hosts had the better chances throughout as Fabian Ruiz and Arkadiusz Milik had shots saved by Liverpool goalkeeper Alisson.
“We have to blame ourselves, that’s how it is,” said Klopp.
Liverpool’s best effort came via Mohamed Salah, who shot wide after the break, but Klopp’s side failed to record a single effort on target in Italy.
Home goalkeeper David Ospina reacted quickly to prevent Sadio Mane and Salah running on to through-balls late on.
But Napoli winger Jose Callejon’s volley was also kept out later in the second half.
“There’s no problem, the boys did a brilliant job tonight,” added Klopp. “They tried everything and were really busy, but not smart enough or calm enough in the right moments.
“When that happens, you lose football games.”
“We had our moments, but too often the formation was not right or we moved in the wrong spaces. The job of the midfield three was nearly impossible. You have to stay calm in a situation like that, but we were too hectic with the ball.
“We had good moments, but not enough. A 0-0 away from home is OK, but we made a mistake before their goal. That’s the second time this season that we have conceded a goal like that.
“It was intense, but we caused the intensity of the game ourselves. It was an interesting looking group before we started and it’s still interesting now. We want to play better than we did tonight, but even if we don’t play brilliantly, we want a result. Tonight we weren’t as good as we could be.”